Template subclass virtual override

I have a question for C++ gurus

Assuming I have template class:

   template <class T>
   class Car<T>
   {
       Car();
       virtual T* factory();
   }

   template <class T>
   T*
   Car::factory()
   {
       return new T;
   }

Here is a class I will use to drive T above:

  class Airplane
  {
         Airplane();
  }

To use like this:

  Car<Airplane> myCar;
  Airplane* a = myCar.factory();

Fine so far. Now let's say I want to subclass my template to provide
an ovreride to the factory method because I don't want to allow a
default constructor of Airplane, but rather a one arg constructor:

   class Spaceship
   {
       Spaceship(int arg);
    private:
       Spaceship(); // to prevent being able to instantiate without
arg
   }

And finally a subclass of the template that overrides the virtual
factory method:

class Boat : public Car<Spaceship>
{
       Boat();
       virtual Spaceship* factory();
}

   Spaceship*
   Boat::factory()
   {
       return new Spaceship(100);
   }

In theory to use like this:

   Boat<Spaceship> myBoat;
   Spaceship* a = myBoat.factory();

The above does not quite compile because when the compiler uses
Spaceship to generate the Boat<Airplane> class from the template,
which is really a subclass of Car, it expects to find a default
constructor for the Spaceship class in order to satisfy the template
base class virtual factory method, even though there are no clients
that will use Car<Spaceship>, only Boat<Spaceship>

I really need Car() to have this default factory method for cases
where people will not use a subclass or override that virtual factory
method, like my first example of Car<Airplane>. However, I also in
this case don't want to provide a default constructor to my Spaceship
class because it will NEVER be used that way and I want to make sure
it can't be used that way.

Can anyone think of a way to satisfy the template without having to
add the default constructor to Spaceship? Or perhaps a different
class structure that will accomplish what I'm trying to do. ??